Counting Lattice Paths Using Fourier Methods (Lecture Notes in Applied and Numerical Harmonic Analysis) - Tapa blanda

Sinopsis

<DIV>THIS MONOGRAPH INTRODUCES A NOVEL AND EFFECTIVE APPROACH TO COUNTING LATTICE PATHS BY USING THE DISCRETE FOURIER TRANSFORM (DFT) AS A TYPE OF PERIODIC GENERATING FUNCTION. UTILIZING A PREVIOUSLY UNEXPLORED CONNECTION BETWEEN COMBINATORICS AND FOURIER ANALYSIS, THIS METHOD WILL ALLOW READERS TO MOVE TO HIGHER-DIMENSIONAL LATTICE PATH PROBLEMS WITH EASE. THE TECHNIQUE IS CAREFULLY DEVELOPED IN THE FIRST THREE CHAPTERS USING THE ALGEBRAIC PROPERTIES OF THE DFT, MOVING FROM ONE-DIMENSIONAL PROBLEMS TO HIGHER DIMENSIONS. IN THE FOLLOWING CHAPTER, THE DISCUSSION TURNS TO GEOMETRIC PROPERTIES OF THE DFT IN ORDER TO STUDY THE CORRIDOR STATE SPACE. EACH CHAPTER POSES OPEN-ENDED QUESTIONS AND EXERCISES TO PROMPT FURTHER PRACTICE AND FUTURE RESEARCH. TWO APPENDICES ARE ALSO PROVIDED, WHICH COVER COMPLEX VARIABLES AND NON-RECTANGULAR LATTICES, THUS ENSURING THE TEXT WILL BE SELF-CONTAINED AND SERVE AS A VALUED REFERENCE.</DIV><DIV><BR></DIV><DIV><I>COUNTING LATTICE PATHS USING FOURIER METHODS</I> IS IDEAL FOR UPPER-UNDERGRADUATES AND GRADUATE STUDENTS STUDYING COMBINATORICS OR OTHER AREAS OF MATHEMATICS, AS WELL AS COMPUTER SCIENCE OR PHYSICS. INSTRUCTORS WILL ALSO FIND THIS A VALUABLE RESOURCE FOR USE IN THEIR SEMINARS. READERS SHOULD HAVE A FIRM UNDERSTANDING OF CALCULUS, INCLUDING INTEGRATION, SEQUENCES, AND SERIES, AS WELL AS A FAMILIARITY WITH PROOFS AND ELEMENTARY LINEAR ALGEBRA.</DIV>

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